Homomorphic encryption schemes are described in cryptographic literature. However, in practice, such schemes are considered impractical and inefficient, and therefore are typically neglected. Fully homomorphic encryption schemes, at the present time, tend to require heavy computational resources, hence, the reputation of such schemes as being impractical, in contrast to other schemes which require the ciphertext to be decrypted, the calculations then performed on plaintext and the results of the calculations re-encrypted. Homomorphic encryption schemes have the advantage that calculations may be performed on ciphertext data without a need to decrypt the ciphertext, perform the calculations on plaintext, and then to re-encrypt the result of the calculations.
Homomorphic encryption schemes that can perform only a limited number of homomorphic operations are referred to in the art as “Somewhat Homomorphic Encryption schemes” (SHE).